The use of a GPGPU programming paradigm (running CUDA-enabled algorithms on GPU cards) in biomedical engineering and biology-related applications have shown promising results. GPU acceleration can be used to speedup computation-intensive models, such as the mathematical modeling of biological systems, which often requires the use of nonlinear modeling approaches with a large number of free parameters. In this context, we developed a CUDA-enabled version of a model which implements a nonlinear identification approach that combines basis expansions and polynomial-type networks, termed Laguerre-Volterra networks and can be used in diverse biological applications. The proposed software implementation uses the GPGPU programming paradigm to take advantage of the inherent parallel characteristics of the aforementioned modeling approach to execute the calculations on the GPU card of the host computer system. The initial results of the GPU-based model presented in this work, show performance improvements over the original MATLAB model.